THE GLOBAL SOLUTION AND BLOWUP OF A SPATIOTEMPORAL EIT PROBLEM WITH A DYNAMICAL BOUNDARY CONDITION∗

doi:10.1007/s10473-023-0425-8

摘要/Abstract

摘要： We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical exponent. There are three major ingredients in this paper. The first is the finite time blowup and the decay estimate of the global solution with a lower-energy initial value. The second ingredient is the $L^q(2\leq q<\infty)$ estimate of the global solution applying the Moser iteration, which allows us to show that any global solution is a classical solution. The third, which is the main ingredient of this paper, explores the long time asymptotic behavior of global solutions close to the stationary solution and the bubbling phenomenons by means of a concentration compactness principle.

关键词: spatiotemporal EIT problem, fractional Dirichlet-to-Neumann operator, critical exponent, bubbling phenomena

Abstract: We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical exponent. There are three major ingredients in this paper. The first is the finite time blowup and the decay estimate of the global solution with a lower-energy initial value. The second ingredient is the $L^q(2\leq q<\infty)$ estimate of the global solution applying the Moser iteration, which allows us to show that any global solution is a classical solution. The third, which is the main ingredient of this paper, explores the long time asymptotic behavior of global solutions close to the stationary solution and the bubbling phenomenons by means of a concentration compactness principle.

Key words: spatiotemporal EIT problem, fractional Dirichlet-to-Neumann operator, critical exponent, bubbling phenomena

Minghong XIE, Zhong TAN. THE GLOBAL SOLUTION AND BLOWUP OF A SPATIOTEMPORAL EIT PROBLEM WITH A DYNAMICAL BOUNDARY CONDITION^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1881-1914.

Minghong XIE, Zhong TAN. THE GLOBAL SOLUTION AND BLOWUP OF A SPATIOTEMPORAL EIT PROBLEM WITH A DYNAMICAL BOUNDARY CONDITION^∗[J]. Acta mathematica scientia,Series B, 2023, 43(4): 1881-1914.

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THE GLOBAL SOLUTION AND BLOWUP OF A SPATIOTEMPORAL EIT PROBLEM WITH A DYNAMICAL BOUNDARY CONDITION^∗

THE GLOBAL SOLUTION AND BLOWUP OF A SPATIOTEMPORAL EIT PROBLEM WITH A DYNAMICAL BOUNDARY CONDITION^∗

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